What is a natural notion of distance between power spectral density functions?

Tryphon T. Georgiou

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

We introduce a Riemannian metric on the cone of spectral density functions of discrete-time random processes. This is motivated by a problem in prediction theory, and it is analogous to the Fisher information metric on simplices of probability density functions. Interestingly, in either metric, geodesics and geodesic distances can be characterized in closed form. The goal of this paper is to highlight analogies and differences between the proposed differential-geometric structure of spectral density functions and the information geometry of the Fisher metric, and raise the question as to what a natural notion of distance between power spectral density functions is.

Original languageEnglish (US)
Title of host publication2007 European Control Conference, ECC 2007
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages358-361
Number of pages4
ISBN (Electronic)9783952417386
StatePublished - Jan 1 2007
Event2007 9th European Control Conference, ECC 2007 - Kos, Greece
Duration: Jul 2 2007Jul 5 2007

Publication series

Name2007 European Control Conference, ECC 2007

Other

Other2007 9th European Control Conference, ECC 2007
CountryGreece
CityKos
Period7/2/077/5/07

Keywords

  • Spectral geometry
  • information geometry

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